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New iterative technique for solving a system of nonlinear equations

Author

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  • Noor, Muhammad Aslam
  • Waseem, Muhammad
  • Noor, Khalida Inayat

Abstract

Various problems of pure and applied sciences can be studied in the unified frame work of the system of nonlinear equations. In this paper, a new family of iterative methods for solving a system of nonlinear equations is developed by using a new decomposition technique. The convergence of the new methods is proved. Efficiency index of the proposed methods is discussed and compared with some other well-known methods. The upper bounds of the error and the radius of convergence of the methods are also found. For the implementation and performance of the new methods, the combustion problem, streering problem and Van der Pol equation are solved and the results are compared with some existing methods. Several new iterative methods are derived from the general iterative scheme. Using the ideas and techniques of this paper, one may be able to suggest and investigate a wide class of iterative methods for solving the system of nonlinear equations. This is another direction of future research.

Suggested Citation

  • Noor, Muhammad Aslam & Waseem, Muhammad & Noor, Khalida Inayat, 2015. "New iterative technique for solving a system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 446-466.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:446-466
    DOI: 10.1016/j.amc.2015.08.125
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    1. Noor, Muhammad Aslam & Waseem, Muhammad & Noor, Khalida Inayat & Ali, Muhammad Aamir, 2015. "New iterative technique for solving nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1115-1125.
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    Cited by:

    1. Kamsing Nonlaopon & Awais Gul Khan & Farah Ameen & Muhammad Uzair Awan & Clemente Cesarano, 2022. "Multi-Step Quantum Numerical Techniques for Finding the Solutions of Nonlinear Equations," Mathematics, MDPI, vol. 10(15), pages 1-17, July.
    2. Waseem, Muhammad & Noor, Muhammad Aslam & Noor, Khalida Inayat, 2016. "Efficient method for solving a system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 134-146.
    3. Munish Kansal & Alicia Cordero & Sonia Bhalla & Juan R. Torregrosa, 2020. "Memory in a New Variant of King’s Family for Solving Nonlinear Systems," Mathematics, MDPI, vol. 8(8), pages 1-15, July.

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    1. Kamsing Nonlaopon & Awais Gul Khan & Farah Ameen & Muhammad Uzair Awan & Clemente Cesarano, 2022. "Multi-Step Quantum Numerical Techniques for Finding the Solutions of Nonlinear Equations," Mathematics, MDPI, vol. 10(15), pages 1-17, July.
    2. Waseem, Muhammad & Noor, Muhammad Aslam & Noor, Khalida Inayat, 2016. "Efficient method for solving a system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 134-146.
    3. Munish Kansal & Alicia Cordero & Sonia Bhalla & Juan R. Torregrosa, 2020. "Memory in a New Variant of King’s Family for Solving Nonlinear Systems," Mathematics, MDPI, vol. 8(8), pages 1-15, July.

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